That holds no weight. If there is any kind of discussion with a ref, then play would be already stopped. Therefore it wouldn't be illegal to cross the center line. And it's only illegal to cross the center line if a goalie is making a play on the puck. Goalies cross the center line in the 2nd period if they are skating to the bench on a delayed penalty.

Please don't just make up reasons.

You're right that the Ineligible Player penalty (for playing the puck over centre) doesn't apply, but the Leaving The Crease rule does. Goaltenders aren't even allowed to go to their benches to get water, new sticks, etc, without the referee's permission, and it's generally the captain's responsibility to ask the referee for that permission.